Pareto Solution Set Research Articles

Reactive power and voltage control based on reactive power compensation coefficient and sensitivity factor

Abstract Aiming at the problems that the existing reactive power allocation methods do not take into account the specific operating state of each doubly-fed induction generator (DFIG) and the established optimization model has many variables and is complicated, this paper proposes to construct an optimization model based on reactive power compensation coefficient and sensitivity factor, to reduce the number of variables in the mathematical model and simplify the expression of the relationship between each key parameter, so the speed of the reactive power and voltage control are improved. In the process of constructing specific optimization models, the objective of minimizing the active loss takes into account the operating copper consumption of each DFIG. The objective of minimizing the voltage fluctuation of each DFIG is also taken into account, in addition to the operating state constraints of each DFIG, so that the final reactive power allocation is more practical. In solving the multi-objective optimization problem, the improved NSGA-II algorithm is utilized, which can achieve the simultaneous optimization of multiple objectives, and when combined with the simplified model established in this paper, the correctness and speed of obtaining the optimal solution set of Pareto can be further improved. Finally, the effectiveness of the proposed strategy in reducing active losses and voltage fluctuations in wind farms is verified by simulation examples.

Research on the Carbon Reduction Technology Path of the Iron and Steel Industry Based on a Multi-Objective Genetic Algorithm

This paper establishes a multi-objective optimization model based on an improved NSGA-II algorithm, aiming to study the carbon reduction technology path of specific enterprises in the steel industry under the background of China’s dual-carbon goal and fill the research gap in the carbon reduction technology path of steel enterprises, which has certain guiding significance for the realization of China’s dual-carbon goal and the low-carbon development of steel enterprises. Firstly, through the analysis of the list of extreme energy efficiency technologies in the steel industry and the main process flow of steel industry production, the multi-objective optimization model is constructed from the two objective dimensions of maximum CO2 emission reduction and maximum enterprise economic benefit. Then the improved NSGA-II algorithm is used to solve the model. And the empirical analysis of a Hebei iron and steel enterprise, based on the technology application of enterprises before the release of the technology list, the technology path of enterprises to reduce carbon is predicted. The actual application data of the enterprise is used for verification and analysis, and suggestions on the technical path for the future low-carbon development of the enterprise are provided. The experimental results show that: (1) The optimal solution set of Pareto is consistent with the practical application of enterprises, and the constructed model is accurate and efficient, which can be used for the research of carbon reduction technology path. (2) When introducing technology, enterprises can give priority to the solution of common set technology based on their own needs.

Low-carbon-oriented commercial district urban form optimization and impact assessment analysis

Commercial buildings have become one of the main sources of carbon emissions. However, the current research on urban form optimization has lacked analyses of the low-carbon indicators of buildings. With the Beijing commercial district as an example, a low-carbon-oriented urban form optimization path is established in this study, and a new method of urban form optimization is developed from a low-carbon perspective. With the help of the parametric platform and multiobjective optimization algorithm, a dynamic optimization model of urban morphology based on parametric modeling, numerical simulation and algorithm optimization is developed, and the morphological characteristics of low-carbon commercial blocks in Beijing are assessed with a Pareto-optimal solution set. Through principal component regression analysis, the correlations between urban form factors and low-carbon evaluation indicators are discussed. The study shows that the multiobjective optimization algorithm effectively optimizes the low-carbon indicators of buildings at the block scale. The urban forms obtained from the Pareto solution set display several commonalities reflected from three perspectives: building type, vertical dimension and building orientation. It is found that the optimal block layout form reduces the building carbon emission intensity and the building outer skin radiation difference, and the renewable energy-based carbon reduction is large. The urban form factors that have a significant impact on the carbon emission intensity of buildings include the maintenance coefficients, the average area to perimeter ratio, and the sky view factor, with respective impact coefficients of 0.301, −0.309, and −0.319.

Optimization of multi-staged Tesla valve using response surface methodology

The multi-stage Tesla valve (MSTV), which consists of multiple identical TVs in series, enhances the effectiveness of the TV. To further improve the performance of the MSTV, an improved MSTV has been proposed by designing each arch channel in the typical MSTV as two separate arch channels: the inner arch channel and the outer arch channel. Response surface methodology is used to optimize the improved MSTV, with the maximum mass flow rate in forward flow and the minimum mass flow rate in reverse flow as two optimization objectives. The non-dominated sorting genetic algorithm is employed to obtain the Pareto solution set, resulting in the optimized design for the improved MSTV (named short-baffle improved MSTV). Theoretical simulations and experimental research are conducted on a typical MSTV, an improved MSTV, and a short-baffle improved MSTV, and their flow resistance ratios (FRRs) are obtained. The FRR of the short-baffle improved MSTV has improved by an average of 8.70% compared to that of typical MSTV. At low inlet pressures, the increase in FRR is approximately 1.4% higher than that at high inlet pressures. The research results indicate that the FRR of the shot-baffle improved MSTV is greater than that of a typical MSTV, and to some extent, the performance of an MSTV is enhanced under low inlet pressure.

A two-objective-optimization-driven group decision making model under the bipolarity of decision information

When building consensus in group decision making (GDM) under uncertainty, an important yet rarely studied issue is to find the Pareto solutions of multi-objective optimization model. This paper reports a two-objective (2Ob) optimization driven consensus model in GDM by describing the bipolarity of judgements through intuitionistic multiplicative preference relations (IMPRs). First, it is realized that the inherent property of IMPRs is the hesitancy degree. A novel inconsistency index of IMPRs is proposed by combining the effects of hesitancy degree and inconsistency of boundary matrices. Second, the compatibility measure between two IMPRs is utilized to quantify the consensus level (CL) of decision makers. The threshold of acceptable group CL is found to decrease with the order of IMPRs for the first time. A 2Ob optimization model is constructed by minimizing group inconsistency degree and group CL, respectively. Third, the method of equipping two flexibility degrees to each expert is proposed for optimizing individual IMPRs. It is interesting to find that the constructed granularity matrix is different from interval-valued IMPRs. A multi-objective particle swarm optimization algorithm is adopted to obtain a set of Pareto solutions to GDM problems. Case studies are carried out to illustrate the proposed consensus reaching model. The results help to identify how to provide flexible decisions in GDM under some complexity and uncertainty of a practical problem.

MORSA: Multi-objective reptile search algorithm based on elite non-dominated sorting and grid indexing mechanism for wind farm layout optimization problem

The proposal of the wind farm layout optimization (WFLO) problem aims to better utilize wind energy. A multi-objective reptile search algorithm (MORSA) based on elite non-dominated sorting and grid indexing mechanism was proposed to solve the multi-objective optimization problem of wind farm layout under the Jansen wake model to maximize power generation while minimizing costs. Firstly, the elite non-dominated sorting method was used to sort the population, and then the crowding distance method was used to maintain the diversity between the optimal sets. By calculating the crowding distance, the same level of non-dominated populations are sorted. Then, the grid index mechanism is added to the archive for selection and deletion. Leaders can use the roulette wheel to select and delete some solutions in high-density grids. By obtaining the optimal Pareto solution set while maintaining the diversity of the population, the effectiveness of solving multi-objective optimization problems is improved. The improved algorithm solves the WFLO problem based on the Jansen wake model by using two different initial self-flow winds for performance testing while considering the effects of single wake and multiple wake with or without partial wake occlusion. The performance of the WFLO (output power and cost) was compared without considering wake obstruction, MORSA can obtain the minimum turbine cost of 26.3601 and the maximum power generation of 2.3078E-08 with a single wake flow of 16 m/s. The experimental results show that the proposed MORSA has better convergence and applicability, and has shown good results in multi-objective layout optimization of wind farms.

A low-carbon economic dispatch method for regional integrated energy system based on multi-objective chaotic artificial hummingbird algorithm

This paper investigates Regional Integrated Energy Systems (RIES), emphasizing the connection of diverse energy supply subsystems to address varied user needs and enhance operational efficiency. A novel low-carbon economic dispatch method, utilizing the multi-objective chaotic artificial hummingbird algorithm, is introduced. The method not only optimizes economic and environmental benefits but also aligns with "carbon peak and carbon neutrality" objectives. The study begins by presenting a comprehensive low-carbon economic dispatch model, followed by the proposal of the multi-objective chaotic artificial hummingbird algorithm, crucial for deriving the Pareto frontier of the low-carbon economic dispatch model. Additionally, we introduce a TOPSIS approach based on combined subjective and objective weights, this approach harnesses the objective data from the Pareto solution set deftly, curbs the subjective biases of dispatchers effectively and facilitates the selection of an optimal system operation plan from the Pareto frontier. Finally, the simulation results highlight the outstanding performance of our method in terms of optimization outcomes, convergence efficiency, and solution diversity. Noteworthy among these results is an 8.8% decrease in system operational economic costs and a 14.2% reduction in carbon emissions.

Multi-objective optimization design of scramjet nozzle based on grey wolf optimization algorithm and kernel extreme learning machine surrogate model

This study delves into the parametric design of the scramjet nozzles, utilizing the Catmull–Rom curve, to meet the high-performance design requirements. It establishes a high-dimensional, multi-objective optimization design method based on a surrogate model for the nozzle. In addition, this research proposes a surrogate model for nozzle performance to enhance the accuracy of the traditional surrogate model and prevent the multi-objective optimization design method from optimizing in an incorrect direction. This model incorporates the grey wolf optimization (GWO) algorithm and kernel extreme learning machine (KELM). Various machine learning algorithms are compared and analyzed, demonstrating that the performance parameters predicted by the GWO-KELM model are the most accurate, and the generalization of GWO-KELM is verified. Utilizing the particle swarm optimization algorithm assisted by GWO-KELM, the multi-objective optimization of the nozzle is further investigated. This study obtains the optimal Pareto front, analyzes the distribution of design variables in the Pareto solution set, and reveals the impact of geometric parameters on nozzle performance. Comparing the representative nozzle from the Pareto front with the truncated maximum thrust nozzle, it is found that the thrust, lift, and outlet Mach number increase by 3.3%, 12.2%, and 0.5%, respectively, while the outlet height decreases by 5.3%. This research contributes to overcoming the limitations of traditional design methods, which are typically time-consuming. The proposed GWO-KELM surrogate model effectively tackles the issue of low prediction accuracy.

Multi-objective particle swarm optimization algorithm based on multi-strategy improvement for hybrid energy storage optimization configuration

In order to fully leverage the advantages of hybrid energy storage systems in mitigating voltage fluctuations, reducing curtailment rates of wind and solar power, minimizing active power losses, and enhancing power quality within distributed generation systems, while effectively balancing the economic and security aspects of the system, this paper establishes a multi-objective hybrid energy storage optimization configuration model that comprehensively considers the lifecycle economic costs, node voltage deviations, and system active power losses. To address the limitations of single-objective solution algorithms and the lack of diversity and premature convergence in multi-objective optimization processes, a multi-objective particle swarm optimization by multi-strategy improvements (CMOPSO-MSI) is proposed to solve the model. By introducing adaptive grid crowding distance and roulette wheel selection strategies to dynamically update the Pareto solution set, population uniformity and diversity are ensured. An improved dynamic nonlinear weighting strategy is introduced to enhance the algorithm's global search capability and convergence performance. A Gaussian mutation strategy is incorporated into the iteration process to enhance the uniformity of non-dominated solutions and particle search capabilities The aim is to achieve an optimal balance between the configuration cost and stability of hybrid energy storage systems. A simulation analysis under multiple cases is performed, taking an IEEE 33-node power distribution system as an example, with introducing photovoltaic and wind energy sources. The results demonstrate that the proposed algorithm achieves better Pareto frontiers and convergence performance compared to conventional multi-objective particle swarm optimization algorithms MOPSO, and classical multi-objective optimization algorithm NSGA-II, validating the effectiveness and accuracy of the proposed model and algorithm strategies in solving the hybrid energy storage optimization configuration problems. The approach concurrently considers system economics and grid stability while improving power quality.

Multiple-Zone Synchronous Voltage Regulation and Loss Reduction Optimization of Distribution Networks Based on a Dual Rotary Phase-Shifting Transformer

For the problem in which accessing a high proportion of renewable energy results in exceeding the limit in distribution network voltage, the existing regulating method experiences difficulty in considering the two-way voltage regulation and loss reduction optimization function. This study proposes a series-type dual rotary phase-shifting transformer (DRPST) based on the principle of phase volume synthesis. This transformer exhibits bidirectional voltage regulation, high reliability, and low cost. First, the topology, operating principle, and equivalent circuit of DRPST are introduced, and its simplified circuit model is established. On the basis of this model, the causes of voltage exceeding the limits are analyzed and the active distribution network model that contains DRPST is constructed. A real-time rolling two-layer optimization strategy based on DRPST is proposed. The inner layer model is solved using the multi-objective particle swarm optimization algorithm with the objective of minimizing voltage deviation and line loss. The optimal compromise solution of the Pareto solution set of the inner layer model is determined using the fuzzy subordinate degree function method. The outer model is based on the optimal compromise solution of the inner model, and the DRPST output rotor angle is controlled without deviation through double closed-loop proportional–integral regulation. Finally, the correctness and effectiveness of the proposed topology and control method are verified via simulation and experimental analysis.

Research on Green Building Design Optimization Based on Building Information Modeling and Improved Genetic Algorithm

The energy consumption of the construction industry has been increasing year by year, posing a huge challenge to China’s dual carbon goals of peaking carbon emissions and achieving carbon neutrality. The Chinese construction industry has huge potential for energy conservation and emission reduction, and the government has therefore put forward requirements for constructing green buildings and formulated strict evaluation standards. The carbon emissions of the construction industry involve various stages of the entire life cycle and are closely related to the green building design standards that meet the requirements. This article sets multiple objective functions based on the two dimensions of the carbon emissions of the entire life cycle of buildings and green building evaluation and uses the NSGA-II algorithm in genetic algorithms to optimize ten indicators selected from the two objectives. Based on this, building information modeling (BIM) modeling was carried out for an office building project in Southwest China, and energy consumption analysis and evaluation were conducted based on the project’s multidisciplinary model. The dialectical relationship between the carbon emissions of the entire life cycle of buildings and the green building evaluation values was discovered, and the optimized parameter combination scheme corresponding to the Pareto solution set was obtained, providing a reference for using improved genetic algorithms and BIM technology to optimize green building design.

Study on the Optimization of Wujiang’s Water Resources by Combining the Quota Method and NSGA-II Algorithm

Recently, the Chinese government has implemented stringent water requirements based on the concept of ‘Basing four aspects on water resources’. However, existing research has inadequately addressed the constraints of water resources on population, city boundaries, land, and production, failing to adequately analyze the interplay between water resource limitations and urban development. Recognizing the interconnectedness between urban water use and economic development, a multi-objective model becomes crucial for optimizing urban water resources. This study establishes a nonlinear multi-objective water resources joint optimization model, aligning with the “Basing four aspects on water resources” requirement to maximize urban GDP and minimize total water use. A genetic algorithm (NSGA-II Algorithm) is applied to solve this complex nonlinear multi-objective model and obtain the Pareto solution set, addressing information loss inherent in the traditional water quota method. The model was tested in Wujiang District, an area located in China’s Jiangsu Province that has been rapidly urbanizing over the past few decades, and yielded 50 non-inferior water resource optimization schemes. The results reveal that the Pareto solution set visually illustrates the competition among objectives and comprehensively displays the interplay between water and urban development. The model takes a holistic approach to consider the relationships between water resources and urban population, land use, and industries, clearly presenting their intricate interdependencies. This study serves as a valuable reference for the rational optimization of water resources in urban development.

Long-term multi-objective optimal scheduling for large cascaded hydro-wind-photovoltaic complementary systems considering short-term peak-shaving demands

The effective synergy among hydropower, wind power, and photovoltaic enhances variable renewable energy (VRE) utilization. However, existing long-term hydropower operating rules that consider runoff uncertainty neglect escalating peak-shaving demands. This paper optimizes the long-term decision-making of hydropower by supplementing the demand to buffer short-term VRE uncertainty. Latin hypercube sampling and K-means clustering reduction are utilized to generate coupling scenario sets to quantify long-term runoff and short-term VRE uncertainties. Then, a double-layer multi-objective optimization model is developed, the outer layer maximizes the long-term expected energy production of the whole system, and the inner layer minimizes hourly residual load fluctuation of power grids under daily electricity boundaries. The daily electricity is dependent on the load profile and monthly generation. Moreover, A power-electricity coupling approach is proposed to bridge long- and short-term operations and reduce the computational burden. An optimal set of pareto solutions is finally obtained with different constraint boundaries, where a compromise solution is selected by a fuzzy decision method. The model has been implemented on the Lancang River hydro-wind-photovoltaic complementary system in Southwest China. The results indicate that: (1) the model can transfer hydropower electricity from flood season to dry season, facilitate VRE integration, increase overall benefits, and improve short-term hydropower regulation capacity, especially in wet years; (2) the obtained Pareto solution set has significant advantages. Under multi-year average conditions, energy production increases by 11 million kWh, hydropower curtailment decreases by 751 million kWh, and residual load fluctuations reduce by 2200 MW, and (3) increasing transmission capacity is more conducive to improving system efficiency in wet years than in dry years, and is helpful to enhance hydropower flexibility.

Bionic topology optimization design and multi-objective optimization of guide arm

Lightweight design is universally recognized as a critical criterion for many engineering problems. In addition to the well-developed topology optimization (TO) method, structural bionics is also considered an effective approach to developing innovative structure designs with lightweight. In the process of natural evolution, bamboo has developed a unique hollow structure with ingenious mechanical properties. Inspired by these characteristics, this paper selected bamboo as a bionic prototype to carry out bionic structure optimization of guide arm. First, the initial guide arm was modeled and simulated for its mechanical behavior. Secondly, similarity analysis between bamboo and guide arm was performed from three aspects, and the parametric bionic guide arm model was established step by step. Then, the key parameters affecting the performance of the bionic guide arm were verified by the parameter sensitivity analysis method. The multi-objective optimization was carried out with the minimum of the total mass and the maximum deformation of guide arm as the optimization objectives. The optimal solution of Pareto solution set was determined by multi-objective decision methods of the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and Gray Relational Analysis (GRA). Finally, finite element (FE) method was used to make a comparison between the initial model and the optimal bionic model in terms of mechanical performance. According to the results, under the premise of the mass of the optimized bionic model decreased by 17.44%, the maximum deformation was decreased by 9.24%, the equivalent stress was decreased by 17.33%, and the first-order frequency was increased by 22.92%. Comparison results showed that the proposed bionic model provided the best lightweight solution for guide arm. This study reveals that structural bionics provides a new solution for the lightweight design of guide arm and similar beam structural components.

Multi-objective optimization design of a cobweb-like–channel heat sink using particle swarm algorithm

Abstract The cobweb-like microchannel heat sink is acknowledged for its exceptional heat transfer capabilities in comparison to other biomimetic microchannel heat sinks. The objective of this paper is to improve the performance of the cobweb-like microchannel heat sink by optimizing its geometric structure parameters through a multi-objective approach. The Box-Behnken design method was utilized to conduct response surface analysis on the design variables, and the Pareto solution set was obtained by applying the multi-objective particle swarm optimization algorithm to the fitted functions of pressure and temperature. The TOPSIS method was used to select the most appropriate solution from the Pareto solution set. The performance of a microchannel heat sink was evaluated using the computational fluid dynamics (CFD) analysis. The optimized structure of the cobweb-like microchannel heat sink led to a decrease in the average temperature by 3K and a reduction in pressure drop by 1514Pa, as compared to the original design. This significant improvement in the overall performance highlights the importance of a well-designed channel structure in further enhancing the comprehensive performance of the microchannel heat sink.

Optimal power flow research of AC–DC hybrid grid with multiple energy routers

AC/DC hybrid grids are the future development trends of grids, and energy routers (ERs) can play key roles in controlling power flow, realizing the regulation of electric energy and improving power quality in the grids. At present, there have been many studies on the structure and control strategy of ERs, but only a few studies are on the power flow distribution and optimization of AC/DC hybrid grids with ERs. To enhance the efficacy of ERs in system-wide regulation and operational optimization, a multi-objective optimal power flow model is formulated for AC–DC hybrid systems with multiple ERs. In order to make ERs play a better role in overall regulation and operation optimization, the multi-objective optimal power flow model of AC–DC hybrid system with multi-ERS is established based on Newton–Raphson method (NR) and alternating iteration method with power consumption and voltage deviation as optimization objectives. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) is used to optimize the model, and a smoother Pareto solution set is obtained compared with multi-objective particle swarm optimization (MOPSO). Then, fuzzy membership method is used to make compromise decision on the Pareto solution set to obtain the optimal compromise solution. Simulation and analysis on an enhanced IEEE 69 bus system verifies the validity of the model. In addition, the results obtained from the compromise solution are compared with the optimization results of MOPF obtained by MOPSO and that of single-objective power flow (SOPF) obtained by Particle Swarm Algorithm (PSO) in the same system. It is proved that the optimization model established can achieve the optimization objectives of reducing voltage deviation and power loss simultaneously to improve the overall performance of the system and optimize the operation state of the system.

Simulation calculation of fluid field- thermal field of oil-immersed transformer and optimization of winding structure parameters

The optimization method of winding structure parameters of oil-immersed transformer is proposed to reduce the hot spot temperature of transformer and the metal conductor consumption based on the coupling calculation method of electromagnetic-fluid-thermal. Firstly, according to the electrical and structural parameters of the oil-immersed transformer, a 3D simulation model is established by using finite element software, and the distribution of the thermal field and the fluid field around the transformer as well as the fluid field and thermal field of the low-voltage winding are obtained. In order to accurately reflect the temperature rise distribution characteristics of the low-voltage winding, a 2D model of the low-voltage winding of the transformer was established considering the calculation efficiency and accuracy, and the thermal field and fluid field distribution of the two low-voltage winding models were compared and analyzed. The temperature error was less than 5.98?, which verified the accuracy of the equivalent model. On this basis, the hot spot temperature of low voltage winding under different structural parameters is obtained by combining the Latin hypercube experiment design and thermal field simulation method, and the response surface model of winding hot spot temperature and structural parameters is established. Taking the hot spot temperature of low voltage winding and the amount of metal conductor as optimization objectives, combined with the response surface model, the optimal solution set of Pareto is obtained by using NSGS-? optimization algorithm, and two kinds of optimal design results are obtained on the Pareto front surface. The results show that the hot spot temperature is reduced by 4.16% and the metal conductor consumption is reduced by 13.79% in scheme 1; the hot spot temperature is reduced by 0.51% and the metal conductor consumption is reduced by 28.46% in scheme 2. The research results have important guiding significance for the optimization of oil-immersed transformer.

Multi-Objective Optimization of a Long-Stroke Moving-Iron Proportional Solenoid Actuator.

In this study, the performance of a long-stroke moving-iron proportional solenoid actuator (MPSA) was improved by combining numerical simulations and experiments. A finite element model of the MPSA was developed; its maximum and mean relative absolute errors of electromagnetic force were 4.3% and 2.3%, respectively, under typical work conditions. Seven design parameters including the cone angle, cone length, depth of the inner hole of the coil skeleton, cone width of the armature, inner cone diameter, and initial position of the moving-iron core were selected for developing the model, and the coefficient of the variation in electromagnetic force, nominal acceleration, 95% of the maximum stable output electromagnetic force, and corresponding response time were used as the performance indicators. The constraint relation between each performance indicator and the influence of each design parameter on the performance indicators were revealed using the uniform Latin hypercube experiment design, correlation analysis, and the main effect analysis method. A multi-objective optimization mathematical model of the MPSA was developed by combining traditional surrogate and machine learning models. The Pareto solution set was obtained using the nondominated sorting genetic algorithm II (NSGA-II), and three decision schemes with different attitudes were determined using the Hurwicz multi-criteria decision-making method. The results showed that a strong contradiction exists among the 95% of the maximum stable output electromagnetic force and its corresponding response time and the coefficient of the variation in electromagnetic force. The cone angle considerably influenced the performance indicators. Compared with the initial design, the coefficient of the variation in electromagnetic force was reduced by 54.08% for the positive decision, the corresponding response time was shortened by 15.65% for the critical decision, and the corresponding acceleration was enhanced by 10.32% for the passive decision. Thus, the overall performance of the long-stroke MPSA effectively improved.

Multi-Objective Short-Term Optimal Dispatching of Cascade Hydro–Wind–Solar–Thermal Hybrid Generation System with Pumped Storage Hydropower

Aiming to mitigate the impact of power fluctuation caused by large-scale renewable energy integration, coupled with a high rate of wind and solar power abandonment, the multi-objective optimal dispatching of a cascade hydro–wind–solar–thermal hybrid generation system with pumped storage hydropower (PSH) is proposed in this paper. Based on the proposed system, the scheduling operation strategy takes into account the complex restrictions of cascade hydropower as well as the flexibility of the PSH. According to various scenarios, the NSGA-II approach is adopted to address the optimization problem, minimizing the system’s residual load variation and operation cost. The Pareto solution sets are contrasted and evaluated, applying the TOPSIS with CRITIC weighting. Additionally, the scheduling output of thermal power, cascade hydropower, and PSH is given in terms of different scenarios. The results demonstrate that the allocation of PSH to a hybrid energy system can significantly reduce the operation cost and the fluctuation in the residual load.

Research on the lightweight design and multilevel optimization method of B‐pillar of hybrid material based on side‐impact safety and multicriteria decision‐making

AbstractThis paper designs and optimizes a new structure hybrid material B‐pillar assembly. Establish a finite element analysis model for the side impact test of an electric vehicle to verify the model's accuracy. Construct a finite element model of the hybrid material B‐pillar assembly. Combined with the static performance analysis of the B‐pillar, the laminate design of the carbon fiber composite B‐pillar reinforcement plate and optimization. For the outer and inner panels of the B‐pillar, the surrogate model method and the multiobjective optimization method are combined to set 11 design variables and 13 responses. The optimal Latin hypercube design method was used to randomly sample each design variable and fit the radial basis function (RBF) approximate model. The modified second‐generation non‐dominated sorting genetic algorithm (MNSGA‐II) was used to carry out multiobjective optimization of the mixed material B‐pillar assembly, and the multicriteria decision‐making method was used to obtain the optimal solution for the Pareto solution set. A drop weight impact test was performed on the hybrid material B‐pillar assembly. The results showed that the peak collision force of the hybrid material B‐pillar was reduced by 43.7% compared with the original steel B‐pillar, the specific energy absorption was increased by 17.5%, and the side impact safety performance was better. After optimization, the weight of the mixed material B‐column was reduced by 26.44%. The improvement rates of the intrusion amount at P2 and the intrusion speed at P1 were 23.99% and 0.63%, respectively, and the lightweight effect and side impact safety were significantly improved.Highlights The finite element analysis parameters of carbon fiber composite materials were constructed through experiments, and the basis for simulation analysis under various working conditions of the B‐pillar based on performance‐driven optimization was established. A hybrid material B‐pillar design method is proposed, which consists of a variable‐thickness high‐strength steel B‐pillar outer plate, a variable‐thickness high‐strength steel B‐pillar inner plate, and a carbon fiber composite B‐pillar reinforcement plate. The super layer of the carbon fiber composite B‐pillar reinforcement plate was optimized and the laying plan of the carbon fiber composite B‐pillar reinforcement plate was determined. Performance‐driven optimization is adopted to realize the collaboration of multilevel design and optimization methods such as B‐pillar conceptual design, detailed design, and multiobjective optimization. A modified NSGA‐II algorithm was proposed and combined with the multicriteria decision‐making method and the entropy‐weighted gray relation analysis method to determine the Pareto optimal solution and the optimal design scheme for the mixed material B‐pillar.